The Lightning Racer is actually a pair of roller coasters. Built in 2000 as the country's first wooden racing coaster, it has made its way onto multiple best-coasters-in-the-country lists. Thunder and Lightning are the two coasters that race each other on two separate, but identical tracks. The only main difference being the staggering of the initial hill. Both roller coasters are initially pulled up the 27.4 meter high hill and then drop down the other side. The 1036.2 meter long tracks of the roller coasters weave in and out of each other, while experiencing changes in speed, direction, and elevation. The ride has no upside down loops, but does contain many twists and turns. The maximum speed achieved on this ride is about 50 mph, or 22.4 m/s. In this experiment, iPhone apps were used both on and off the ride to analyze the physics of both Thunder and Lightning. Conservation of energy is the main element in determining the winner, but factors such as friction, weather, and maintenance influence the ride. The lifts' initial speeds can be controlled by computer at the loading station. This is supposed to be used to ensure that both coasters reach the peak of the hill at the same time, since the hills are staggered, but can affect the winner as well.
A Video of the Ride for your Enjoyment : )
Measured Data:
Initial hill angle: 25 deg
Car seat length: 1.06 m
Car length: 1.24 m
Car length + space between car: 1.29 m
12 cars, 2 riders per car, 24 riders per train
top speed: 22.4 m/s
highest drop: 27.4 m
track length: 1036.32 m
ride duration: 120 s
The graph below represents the velocity components of Thunder (the one that appears to be above the other in the video) while it was being pulled up the initial hill. Video Physics was the app used to film the motion, Logger Pro was used to analyze the motion. Below is also the calculation of the actual velocity using the components.
v^2=vx^2+vy^2
v^2=2.761^2+1.463^2
v^2=9.76
v=3.12 m/s
Below is the graph of Lightning's velocity components as it's being pulled up the initial hill. Video Physics was used to film the motion, Logger Pro was used to analyze it. Also below is the calculated velocity.
v^2=vx^2+vy^2
v^2=2.521^2+1.315^2
v^2=8.085
v=2.84 m/s
The velocity of Thunder was found to be greater than the velocity of Lightning. Since Thunder's hill starts earlier than Lightning's, it shows up in the video later. In order for both coasters to reach the peaks of their respective hills, Thunder should be moving faster on the lift.
The graph below shows the components of the velocity of Lightning as it goes around a curve. Video Physics was the app used to collect and analyze this data. The velocity is calculated below as well.
v^2=vx^2+vy^2
v^2=16.18^2+-.824^2
v^2=262.47
v=16.2 m/s
The graphs below were created using the a-logger app.
Using Conservation of Energy, the velocity at the bottom of the initial hill is calculated below. Since both roller coasters are on identical tracks (ignoring friction and weather conditions), the calculated velocity applies to both Thunder and Lightning. The calculated velocity is then compared to the maximum velocity from Hershey Park's website.
Velocity at the bottom of the first hill:
E1 = E2
PE + KE = PE + KE
PE=KE
mgh = 1/2mv^2
9.8(27.4) = 1/2v^2
v = 23.2 m/s
A Video of the Ride for your Enjoyment : )
Measured Data:
Initial hill angle: 25 deg
Car seat length: 1.06 m
Car length: 1.24 m
Car length + space between car: 1.29 m
12 cars, 2 riders per car, 24 riders per train
top speed: 22.4 m/s
highest drop: 27.4 m
track length: 1036.32 m
ride duration: 120 s
The graph below represents the velocity components of Thunder (the one that appears to be above the other in the video) while it was being pulled up the initial hill. Video Physics was the app used to film the motion, Logger Pro was used to analyze the motion. Below is also the calculation of the actual velocity using the components.
v^2=vx^2+vy^2
v^2=2.761^2+1.463^2
v^2=9.76
v=3.12 m/s
Below is the graph of Lightning's velocity components as it's being pulled up the initial hill. Video Physics was used to film the motion, Logger Pro was used to analyze it. Also below is the calculated velocity.
v^2=vx^2+vy^2
v^2=2.521^2+1.315^2
v^2=8.085
v=2.84 m/s
The velocity of Thunder was found to be greater than the velocity of Lightning. Since Thunder's hill starts earlier than Lightning's, it shows up in the video later. In order for both coasters to reach the peaks of their respective hills, Thunder should be moving faster on the lift.
The graph below shows the components of the velocity of Lightning as it goes around a curve. Video Physics was the app used to collect and analyze this data. The velocity is calculated below as well.
v^2=vx^2+vy^2
v^2=16.18^2+-.824^2
v^2=262.47
v=16.2 m/s
The graphs below were created using the a-logger app.
Using Conservation of Energy, the velocity at the bottom of the initial hill is calculated below. Since both roller coasters are on identical tracks (ignoring friction and weather conditions), the calculated velocity applies to both Thunder and Lightning. The calculated velocity is then compared to the maximum velocity from Hershey Park's website.
Velocity at the bottom of the first hill:
E1 = E2
PE + KE = PE + KE
PE=KE
mgh = 1/2mv^2
9.8(27.4) = 1/2v^2
v = 23.2 m/s
Percent Difference:
(23.2-22.4)/22.4 * 100 = 3.6%